From gov.uk
You do not need to wear a face covering if you have a legitimate reason not to. This includes:
young children under the age of 11
not being able to put on, wear or remove a face covering because of a physical or mental illness or impairment, or disability
if putting on, wearing or removing a face covering will cause you severe distress
if you are travelling with or providing assistance to someone who relies on lip reading to communicate
to avoid harm or injury, or the risk of harm or injury, to yourself or others
to avoid injury, or to escape a risk of harm, and you do not have a face covering with you
to eat or drink, but only if you need to
to take medication
if a police officer or other official requests you remove your face covering.
No mention of a doctor’s note. Just explain you can’t wear one for health reasons if anyone asks.